Fourier Analysis of the Sor Iteration

Abstract

The SOR iteration for solving linear systems of equations depends upon an overrelaxation factor omega. We show that for the standard model problem of Poisson's equation on a rectangle, the optimal omega and corresponding convergence rate can be rigorously obtained by Fourier analysis. The trick is to tilt the space-time grid so that the SOR Successive overrelaxation stencil becomes symmetrical. The tilted grid also gives insight into the relation between convergence rates of several variants. Keywords: Successive overrelaxation,Iterative methods.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1986
Accession Number
ADA211571

Entities

People

  • Lloyd N. Trefethen
  • Randall J. LeVeque

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Convergence
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Formulas (Mathematics)
  • Fourier Analysis
  • Grids
  • Iterations
  • Mathematics
  • Partial Differential Equations
  • Real Variables
  • Security
  • Standards

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)

Technology Areas

  • Space
  • Space - Space Objects